Invariance of the correlation energy at high density and large dimension in two-electron systems

We prove that, in the large-dimension limit, the high-density correlation energy \Ec of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by \Ec \sim -1/(8D^2) for any radial confining potential $V(r)$. This result explains the observed similarity of \Ec in a variety of two-electron systems in three-dimensional space.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Parabolic stable surfaces with constant mean curvature

We prove that if u is a bounded smooth function in the kernel of a nonnegative Schrodinger operator $-L=-(\Delta +q)$ on a parabolic Riemannian manifold M, then u is either identically zero or it has no zeros on M, and the linear space of such functions is 1-dimensional. We obtain consequences for orientable, complete stable surfaces with constant mean curvature $H\in\mathbb{R}$ in homogeneous spaces $\mathbb{E}(\kappa,\tau)$ with four dimensional isometry group. For instance, if M is an orientable, parabolic, complete immersed surface with constant mean curvature H in $\mathbb{H}^2\times\mathbb{R}$, then $|H|\leq 1/2$ and if equality holds, then M is either an entire graph or a vertical horocylinder.Comment: 15 pages, 1 figure. Minor changes have been incorporated (exchange finite capacity by parabolicity, and simplify the proof of Theorem 1)

Anti-Neoplastic Activity of Two Flavone Isomers Derived from Gnaphalium elegans and Achyrocline bogotensis

Over 4000 flavonoids have been identified so far and among these, many are known to have antitumor activities. The basis of the relationships between chemical structures, type and position of substituent groups and the effects these compounds exert specifically on cancer cells are not completely elucidated. Here we report the differential cytotoxic effects of two flavone isomers on human cancer cells from breast (MCF7, SK-BR-3), colon (Caco-2, HCT116), pancreas (MIA PaCa, Panc 28), and prostate (PC3, LNCaP) that vary in differentiation status and tumorigenic potential. These flavones are derived from plants of the family Asteraceae, genera Gnaphalium and Achyrocline reputed to have anti-cancer properties. Our studies indicate that 5,7-dihydroxy-3,6,8-trimethoxy-2-phenyl-4H-chromen-4-one (5,7-dihydroxy-3,6,8-trimethoxy flavone) displays potent activity against more differentiated carcinomas of the colon (Caco-2), and pancreas (Panc28), whereas 3,5-dihydroxy-6,7,8-trimethoxy-2-phenyl-4H-chromen-4-one (3,5-dihydroxy-6,7,8-trimethoxy flavone) cytototoxic action is observed on poorly differentiated carcinomas of the colon (HCT116), pancreas (Mia PaCa), and breast (SK-BR3). Both flavones induced cell death (\u3e50%) as proven by MTT cell viability assay in these cancer cell lines, all of which are regarded as highly tumorigenic. At the concentrations studied (5–80 µM), neither flavone demonstrated activity against the less tumorigenic cell lines, breast cancer MCF-7 cells, androgen-responsive LNCaP human prostate cancer line, and androgen-unresponsive PC3 prostate cancer cells. 5,7-dihydroxy-3,6,8-trimethoxy-2-phenyl-4H-chromen-4-one (5,7-dihydroxy-3,6,8-trimethoxy flavone) displays activity against more differentiated carcinomas of the colon and pancreas, but minimal cytotoxicity on poorly differentiated carcinomas of these organs. On the contrary, 3,5-dihydroxy-6,7,8-trimethoxy-2-phenyl-4H-chromen-4-one (3,5-dihydroxy-6,7,8-trimethoxy flavone) is highly cytotoxic to poorly differentiated carcinomas of the colon, pancreas, and breast with minimal activity against more differentiated carcinomas of the same organs. These differential effects suggest activation of distinct apoptotic pathways. In conclusion, the specific chemical properties of these two flavone isomers dictate mechanistic properties which may be relevant when evaluating biological responses to flavones

Multi-proxy record of Holocene paleoenvironmental conditions from Yellowstone Lake, Wyoming, USA

A composite 11.82 m-long (9876e-67 cal yr BP) sediment record from Yellowstone Lake, Wyoming was analyzed using a robust set of biological and geochemical proxies to investigate the paleoenvironmental evolution of the lake and its catchment in response to long-term climate forcing. Oxygen isotopes from diatom frustules were analyzed to reconstruct Holocene climate changes, and pollen, charcoal, diatom assemblages, and biogenic silica provided information on terrestrial and limnological responses. The long-term trends recorded in the terrestrial and limnic ecosystems over the last 9800 years reflect the influence of changes in the amplification of the seasonal cycle of insolation on regional climate. The early Holocene (9880e6700 cal yr BP) summer insolation maximum and strengthening of the northeastern Pacific subtropical high-pressure system created warm dry conditions and decreasing summer insolation in the middle (6700e3000 cal yr BP) and late (3000e-67 cal yr BP) Holocene resulted in progressively cooler, wetter conditions. Submillenial climate variation is also apparent, with a wetter/cooler interval between 7000 and 6800 cal yr BP and warmer and/or drier conditions from 4500 to 3000 cal yr BP and at ca. 1100 cal yr BP. These data show that the Yellowstone Lake basin had a climate history typical of a summer-dry region, which helps to better define the spatial variability of Holocene climate in the Greater Yellowstone Ecosystem

Correlation energy of anisotropic quantum dots

We study the $D$-dimensional high-density correlation energy \Ec of the singlet ground state of two electrons confined by a harmonic potential with Coulombic repulsion. We allow the harmonic potential to be anisotropic, and examine the behavior of \Ec as a function of the anisotropy $\alpha^{-1}$. In particular, we are interested in the limit where the anisotropy goes to infinity ($\alpha\to0$) and the electrons are restricted to a lower-dimensional space. We show that tuning the value of $\alpha$ from 0 to 1 allows a smooth dimensional interpolation and we demonstrate that the usual model, in which a quantum dot is treated as a two-dimensional system, is inappropriate. Finally, we provide a simple function which reproduces the behavior of \Ec over the entire range of $\alpha$.Comment: 5 pages, 2 figures, 1 table, submitted to Phys. Rev.